2026 年 7 巻 2 号 p. 1-19
This study presents a signal processing and machine learning approach to improve the detection of water path defects in post-tension prestressed concrete (PC) using phased array ultrasonic test (PAUT). In post-tension PC, inadequate grouting can create water paths inside the duct, enabling water pathways and increasing the risk of leakage and tendon corrosion. To address the difficulty of internal inspection, the ultrasonic signal was processed using parasitic discrete wavelet transform (P-DWT), incorporating real mother wavelets (RMWs) generated from finite element simulations. Two RMWs, representing healthy duct and duct with water paths, were used to enhance the characteristic signal patterns of each structural condition. Feature extraction was used to reduce data complexity and simplify it to be more informative. To evaluate the unlabeled data, semi-supervised learning associated with probability-based classification was then performed using a random forest model. The proposed approach demonstrated the method’s reliability in improving the interpretation of PAUT data for structural evaluation. The proposed methodology achieved 90% correct prediction between the two classes with approximately 90% probability, demonstrating improved interpretability compared to the unfiltered signal.
Prestressed concrete (PC) structures, especially with the post-tensioning system, depend on properly grouted tendon duct to ensure structural performance and long-term durability. The grout provides corrosion protection and ensures effective stress transfer between steel tendons and the surrounding concrete. However, insufficient grouting can lead to the development of water paths within the duct, allowing water to enter and travel along the tendon and accelerating the corrosion of prestressing steel1,2). Such deterioration reduces the performance of PC structures and is considered a contributing factor in several failures. Early detection of these grouting conditions is therefore important for structural safety. This study focuses on the water path defect, one of the most common grouting defects in PC tendon ducts3,4). Despite its importance, assessing the internal grouting condition remains challenging5) because the ducts are cast deep within the concrete and cannot be inspected without a destructive test, such as drilling or coring. Although these methods can provide valuable information, they are time-consuming, costly, and may cause localized damage to the structure. Consequently, non-destructive evaluation (NDE) methods have become essential tools for assessing the condition of PC structures.
Numerous NDE techniques have been applied to detect internal defects in PC ducts6,7). However, each presents limitations related to wave behavior, access, and environmental conditions. Impact-Echo (IE) analysis and interpretation involve the simple spectrum analysis8). This technique relies on stress waves that propagate in multiple directions and cannot be effectively focused, limiting its sensitivity to localized defects. Ground-penetrating radar (GPR) cannot detect grouting defects inside metal conduits9). Infrared thermography (IRT) has difficulty detecting defects due to the thick concrete layers surrounding post-tensioned tendon ducts10). Ultrasonic testing is based on applying ultrasonic pulses and analyzing the reflections, or echoes, that return to detect defects like cracks, voids, or corrosion. Early studies demonstrated that ultrasonic NDE can detect voids in tendon ducts through reflections from boundaries between concrete, air, and grout11,12). Phased array ultrasonic testing (PAUT) has become a promising tool over conventional ultrasonic testing (UT) methods for PC duct inspection. PAUT can employ multiple ultrasonic signals inside the material that can be electronically steered and focused to cover a wider region without requiring probe repositioning. This flexibility allows PAUT to adapt beam angles and focus position to optimally interact with materials and defects inside the duct. Based on these capabilities, several studies have shown that PAUT provides enhanced sensitivity to detect defects within the PC duct13–16). However, the complexity of wave propagation in heterogeneous concrete, combined with scattering from aggregates and the presence of steel reinforcement, often produces noisy or ambiguous ultrasonic signals that interfere with the signal interpretation17,18).
To address these adverse effects, recent studies have explored the integration of advanced signal processing and machine learning to enhance ultrasonic defect detection in concrete materials19–21). Wavelet transforms have shown strong potential for analyzing non-stationary signals, enabling decomposition of ultrasonic responses into time-frequency representations that highlight localized anomalies22). Discrete wavelet transforms (DWT) are one of the effective signal processing techniques used to analyze signals for detecting defects in concrete23). However, the mother wavelet (MW) used in the DWT must satisfy a bi-orthogonal condition. Meeting this requirement is challenging, which limits the flexibility in designing the MW. For improvement in detection ability, it is desirable to use the MW whose shape is similar to the signal that is required to be detected. A parasitic discrete wavelet transform (P-DWT) has the flexibility in the design of MW. This allows the use of wavelet that closely resemble the target signal patterns, thereby improving the correlation between the wavelet and the defect-related signal components. As a results, P-DWT enables more effective extraction of localized frequency features associated with scattering and attenuation caused by defects. This improved time-frequency localizations enhances feature discriminability to more reliable defect detection in PAUT-based inspection of PC structure. Nagamatsu et al.24) demonstrated the applicability of P-DWT for anomaly detection in pump signals within a watersteam system, furter supporting its robustness in complex signal environments.
Machine learning further enhances ultrasonic signal analysis by providing automated classification of structural conditions. Random forest classifier, in particular, has shown strong performance in classification due to its robustness against noise, ability to model nonlinear relationships, and effectiveness when dealing with high-dimensional feature spaces25). These advantages are especially relevant for ultrasonic inspection of concrete, where signals often exhibit irregular patterns caused by scattering, attenuation, and heterogeneous material composition. Their framework reduces overfitting by combining multiple decision trees, while integrated feature-importance analysis highlights which signal components contribute most to defect classification. To overcome the limited availability of labeled ultrasonic datasets, where confirmed defect conditions in actual structures are difficult to obtain26), semi-supervised learning can be incorporated to further improve classification performance. Random forest prediction probabilities provide a reliable basis for this process because the probability estimates represent the collective decision of many decision trees, producing a more calibrated confidence score.
The present study proposes an integrated methodology combining P-DWT and semi-supervised learning to improve the detection of water path inside the duct using PAUT. Real mother wavelets (RWMs) representing healthy duct and duct containing water paths were generated using finite element simulation and used to construct P-DWT filters, which were applied to enhance specific characteristics of the ultrasonic signal. Features were extracted to reduce data dimensionality while maintaining important information. A random forest classifier employing probability-based semi-supervised learning was then used to evaluate the PAUT signals. The effectiveness of the proposed method was first evaluated using laboratory specimens with known healthy and water path conditions. This was followed by dismantled specimens obtained from an actual bridge to assess the applicability of the method under field conditions. A final evaluation was performed on dismantled specimens with unclear duct conditions. The classification results were validated through X-ray inspection and ultrasonic image reconstruction, demonstrating that the proposed approach improves the interpretability and accuracy of PAUT analysis of grouting defects.
(1) Specimens
To investigate the detection of water-paths within the PC tendon duct, four PC specimens with dimensions of 450 mm x 350 mm x 220 mm were fabricated, as illustrated in Fig.1a. All specimens were cast using concrete with a compressive strength of 30 – 40 MPa. In real PC structures, water paths often occur when grout is insufficient or poorly injected, allowing continuous voids to remain around the tendon. To recreate this condition experimentally, a 1 mm bundle of paper was inserted inside the duct as an artificial water path. Because the paper has a very low acoustic impedance27), its response is comparable to ungrouted regions.
Two specimens, A-H1 and A-H2, were constructed as healthy specimens. These specimens had a 35 mm diameter duct filled with grout and a single Φ26 rebar within the duct (Fig. 1b). The other two specimens, A-WP1 and A-WP2, had the same configuration but included the artificial water paths attached to the rebar.
To verify the findings from the laboratory tests also apply to real structures, additional samples were taken from part of the Uenae Bridge (Fig. 2). Three field specimens were examined: B-H, which contained a fully grouted duct and was referenced as a healthy specimen (Fig. 2a); B-WP, with a PC duct partially grouted as the water path specimen (Fig.2b). The presence of a water path was confirmed by video documentation showing water was injected into the duct and later flowed out of the duct28). The third specimen is specimen C (Fig. 2c), whose internal condition was uncertain but verified with X-ray results. These bridge samples helped to demonstrate how well the laboratory-based model performs when applied to the more complex and varied conditions in actual PC structures.
(2) PAUT procedures
The modern phased array equipment employs multiple transmitter and receiver units, enabling continuous electronic beam steering and focusing of ultrasonic waves. The phased array sensor consists of a number of ultrasonic probes arranged in an array, connected to the transmitter units by a multicore cable29). The phased array instrument is a computer-controlled unit (Fig.3) with multiple independent channels that apply time delays to each probe, allowing control over beam direction and focal depth while also receiving and processing the reflected signals.
In this study, PAUT was carried out using the setup shown in Fig. 4a and Fig. 4b. Four probes were placed in a straight line with 20 mm spacing between them. Three phased array probes were used as transmitters, and the other probe as the receiver to record the ultrasonic waves traveling through the PC specimens. The broadband vertical probes (B0.05K50x50N) were used in this experiment to generate longitudinal waves at a frequency of 50 kHz, with the wave velocity set to 3,200 m/s. The phased array transmitter was electronically steered to focus at the top of the duct within the concrete. Scanning was performed by moving the probes along the surface of each specimen in small increments, as illustrated by the blue area in Fig. 4c.
For the field setup (Fig. 5), the frequency, wave velocity, and focus point were the same arrangements as the laboratory test; however, due to the accessibility and testing conditions, the test areas were limited, and therefore, the number of data points taken was very low. For the B-H and B-WP specimens, PAUT was performed on both sides (left and right), where each side was taken at three locations as seen at the red line in Fig. 5a and Fig. 5b. As for the specimen C, data was taken from one side at eight measurement locations (red lines). The blue line represents the testing direction and corresponds to the duct location, as illustrated in Fig.6.
Appropriate measures were implemented to ensure reliable acoustic coupling between the concrete surface and the ultrasonic transducers. The test surface was lightly prepared to remove loose particles and minor surface irregularities, thereby improving contact conditions at each measurement point. A gel-type coupling agent was applied between the transducer and the concrete surface to enhance ultrasonic wave transmission and reduce signal attenuation caused by air gaps.
(3) Finite element model
FEM simulations were used to generate a waveform that closely represents the physical conditions for each specimen. A two-dimensional plane-strain solid model was created in PATRAN with material properties in Table 1. The element type used for this model was CPE4 with a mesh size of 2 mm and 0.25 mm around the duct and steel, creating as many as 102,067 elements. For example, Fig.7 shows the laboratory specimen without a water path, the finite element model can be seen in Fig.8, and Fig. 8a shows a portion of the FEM, focusing on the duct region.
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After constructing the model, it was imported to ABAQUS for dynamic analysis. Wave propagation was initiated using a 50 kHZ Ricker wave. As shown in Fig.9, the second wave of FEM analysis, interpreted as a primary reflection, was extracted. This segment of the waveform was then used to construct the RMW.
The RMW is intended to capture the dominant characteristics of the ultrasonic waveform (such as water path defect) rather than all scattering effects caused by material inhomogeneity. Therefore, secondary variations are not essential and do not significantly affect its correlation with the measured signal. Furthermore, to simplify the analysis, the PC was modeled as a solid model. This assumption allows for the generation of a stable and representative waveform, focusing on the dominant propagation behavior rather than the complex scattering effects. Within the P-DWT framework, the RMW serves as a reference pattern of the dominant wave behavior, allowing the RMW to maintain reliable correlation even under moderate variations.
(4) Signal processing
a) Signal segmentation
Signal segmentation was performed to remove the irrelevant signal and keep the meaningful portion that was used for the classification. To make sure that the signal segmentation is relevant to the purpose of classification, the time of flight (ToF) was calculated and used as the basis of segmentation. The ToF represents the arrival time of the first significant ultrasonic pulse.
b) Constructing RMW
RMW was constructed with the procedure as follows: (1) Extract a specific segment of the waveform created from FEM analysis; (2) Multiply the selected waveform by a window function. In this study, a Hanning window was used because it offers better resolution in both the time and frequency domains30); (3) Remove the mean value of the windowed wave to ensure that the waveform is centered around zero; (4) Finally, the waveform is normalized so that its total energy equals one.
c) P-DWT filter
P-DWT is a modified version of the traditional DWT, developed to improve the extraction and identification of meaningful signal features. The method introduces a parasitic filter constructed from an RMW, which is derived from FEM analysis, to capture the characteristic waveform based on the real condition. The P-DWT process is illustrated in Fig. 10 and described as follows. The procedures for designing the parasitic filters: (1) Decomposed and reconstructed the RMW to the level where the parasitic filter will apply. The base mother wavelet used for the decomposition was selected using Akaike information criterion (AIC); (2) Both the approximation and detail coefficients were transformed into the frequency domain using fast fourier transform (FFT). The acquired frequency domain data ;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/ZEq.001.jpg%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
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, real and imaginary parts, are parasitic filters.
After the construction of the parasitic filters, the P-DWT was applied to the target wavelet. The procedures are as follows: (1) Decomposed and reconstructed the target wavelet using the AICselected optimal base wavelet at one level below from the parasitic filters; (2) Approximation and detail coefficients of the target wavelet were converted to the frequency domain using FFT, resulting in ;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/ZEq.003.jpg%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
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; (3) Applied the parasitic filter by multiplying the real and imaginary components of the target signal with the parasitic filters; (4) The modified real and imaginary components were recombined and transformed back to the time domain using inverse FFT (IFFT), resulting in a filtered signal 𝑆𝑙.
(5) Machine learning
a) Feature extraction
Feature extraction was applied to both the unfiltered ultrasonic signal and the filtered signal by P-DWT. The feature extraction was used to reduce the time series data complexity and create new features that keep the important information. Previous studies have employed various feature extraction approaches for ultrasonic signal analysis. For example, wavelet coefficients have been directly used as feature vectors, which results in very high-dimensional input data31). Hu et. al32) selected statistical features such as mean value, standard deviation, kurtosis coefficient, skewness coefficient, and energy ratio to characterize detection signals of concrete defects. Similarly, features such as mean, standard deviation, and kurtosis have been widely used as inputs for an ultrasonic signal classification model33).
Based on commonly used features in ultrasonic testing, this study selects eight statistical features to capture the essential characteristics of ultrasonic signals in both amplitude and distribution domains. These features include mean, standard deviation (std), minimum (min), maximum (max), energy, skewness (skew), kurtosis, and norm. These features were chosen because they effectively represent key statistical properties of the signal that are closely related to ultrasonic wave propagation behavior in concrete. After extraction, feature selection was performed to enhance model performance and reduce redundancy. Selecting top features using mutual information was used to select the highly correlated features-based importance ranking.
b) Semi-supervised learning based on prediction probability
Semi-supervised learning is a machine learning approach that combines labeled data as the training data and uses the unlabeled data for classification. This approach is very practical, especially for the real case specimens with unknown conditions, combined with fabricated laboratory specimens. In this study, the term semi-supervised is used to describe a framework in which the model is trained using labeled laboratory data and then applied to classify the unlabeled data. Although the proposed framework does not involve iterative procedures such as pseudo-labeling or self-training, it reflects a practical semi-supervised scenario. The trained model is therefore used to predict labels for unlabeled data. In addition, the prediction probability function, which is available in many classification algorithms, is utilized to provide not only the predicted class but also the probability associated with each class. This allows for a deeper interpretation of the model’s predictions by revealing how confident the model is in each classification decision.
The algorithm first trains on the labeled data through a random forest classifier (Fig. 11) and then performs label predictions on the unlabeled data. Labeled data were obtained from designated specimens and filtered with RMW based on specimen condition (healthy or water path).
The other specimens were used as the unlabeled data, where each signal was filtered with both healthy and water path RMW, as seen in Fig. 12. These two probability values represent predictions from two different P-DWT interpretations of the same raw signal. After that, the class with the higher probability was chosen as the final predicted label.
This selection represents the most confident interpretation of the signal based on the similarity to either the healthy or water path reference waveforms.
(1) Filtered wavelet
The P-DWT decomposes ultrasonic waveforms into low-frequency and high-frequency components. The unfiltered signal (Fig. 13a) shows the full response of the wave as it travels through the material. The wavelet appears relatively smooth; however, it also means that important details may be hidden by the overall shape, making it difficult to distinguish some features related to material behaviour. After applying P-DWT, the approximate coefficient (P-DWT Lv.1A) (Fig.13b) captured the low-frequency components of a signal. The smoother shape indicates that this component captures the main energy portion of the signal, which aligns with the RMW-based parasitic filter. Level 1 detail coefficient (P-DWT Lv.1D) (Fig. 13c) captures the high-frequency components in the first level of decomposition. This component includes rapid oscillations and spike patterns produced by micro-reflections, small voids, and scattering from inhomogeneities in the concrete. This wavelet is dominated by high-frequency components, which makes it more sensitive to minor changes in the materials. Fig. 13d shows the detail coefficient in the second-level decomposition (P-DWT Lv.2D). The oscillations are less dense but still reflect frequencyrelated behaviour such as wave scattering at interfaces.
The third level of decomposition (P-DWT Lv.3D) is shown in Fig. 13e. This level detail coefficient exhibits lower oscillations and a smoother shape compared with the first and second level of detail coefficients. The waveform shape is similar to P-DWT Lv.1A with smoother fluctuations. Furthermore, the fourth level of detail coefficient (PDWT Lv.4D) (Fig.13f) has a smoother shape and a clearer oscillation pattern.
(2) Analysis of laboratory specimen
a) Evaluation of training data
Fig. 14 shows the performance of a random forest classifier using labeled training data. Training data were collected from A-H2 and A-WP2, and two classes were used: healthy (H) for the specimens without a water path, and water path (WP) for those with water paths. Classifier performance was evaluated by accuracy and k-fold cross-validation with parameters k = 5, and the number of training data was 200. Across the datasets, all features mostly achieved high accuracy, showing high correct predictions for the classification. K-fold cross-validation values estimate how well the model will perform on new, unseen data and detect overfitting. For unfiltered signals, accuracy remained high (0.77-0.99); however, it had lower k-fold cross-validation (0.68-0.88), which showed that classification performance is moderate for the unfiltered signal. When P-DWT filtering was applied, the results showed distinct differences between approximation and detail coefficients. The P-DWT Lv.1A results did not enhance model performance; instead, k-fold cross-validation dropped to 0.57-0.65 across most feature sets, indicating that approximation coefficients contain low-frequency components that are less sensitive to internal changes such as water paths in the PC duct. In contrast, using P-DWT Lv.1D and Lv.2D improved across all feature sets. These levels of decomposition produced the highest k-fold cross-validation scores. Time series (0.97), FE (0.90-0.93), FS3 (0.91-0.92), and FS5 (0.90-0.92), demonstrating that the detail coefficient contains high-frequency components closely associated with scattering, reflections, and other signal changes caused by water paths within the PC duct. However, higher level P-DWT (Lv.3D and Lv.4D) significantly reduced the k-fold cross-validation scores, indicating that smoothing of the waveform may have removed the important information or shifted the signal toward a smoother frequency that reduces class separability.
Using feature extraction and feature selection affected the classification performance, especially for the unfiltered signal and P-DWT Lv.1A, where the kfold cross-validation was lowered across all feature extraction and feature selection, and some of them also lowered the accuracy. However, this did not happen to P-DWT Lv.1D and Lv.2D, where the classification performance remains stable for both accuracy and k-fold cross-validation scores.
b) Semi-supervised learning for laboratory specimens
Semi-supervised learning based on probability prediction was performed in a random forest classifier using data collection from A-H2 and AWP2 as the training data, and A-H1 and A-WP1 as the unlabeled data. For the unlabeled data, each sample contains 20 data signals, where each signal was filtered with both RMW healthy and water path, and can be considered as unlabeled data.
Fig.15 shows the confusion contribution heat map illustrating the number of correct predictions obtained for healthy and water path signals across different representations and P-DWT decomposition levels. The heat map highlights performance consistency and dominant decomposition levels under various feature datasets. Fig. 16 illustrates the prediction probability trend associated with the number of correct predictions. In the time series feature, the unfiltered signals produced an unbalanced prediction, with only 8 correct predictions for the healthy sample and 19 for the water path sample, and prediction probabilities ranging only from 56 – 64%. This demonstrates that the unfiltered signal still contains noise and signal ambiguity that cannot be used to distinguish between two classes.
After applying the P-DWT, the overall performances improved, particularly for the P-DWT Lv.1D and Lv.2D. Prediction probabilities for both classes increased substantially to 97 – 98%, although the number of correct predictions remained unbalanced, with one class exceeding 15 correct predictions while the other had fewer than 10. P-DWT Lv.1A and Lv.4D produced a similar classification trend, achieving a moderate number of correct predictions (12 – 19 across both classes) with prediction probabilities in the range of 64 - 73%. Meanwhile, P-DWT Lv.3D resulted in a strongly unbalanced prediction, with 17 correct predictions for healthy and 4 for water path, with prediction probabilities ranging from 60% - 68%.
When feature extraction (FE) was applied, the classification performance improved compared with using the time series. FE reduced the dimensionality of the data and emphasized the statistical characteristics of the waveform, leading to more stable and discriminative predictions34). For example, with FE, P-DWT Lv.1D and 2D coefficients produced the highest prediction probabilities (87 - 95%) and achieved a balanced number of correct predictions for both classes, with 13 – 15 correct predictions for healthy and 17 – 18 for water path. Although the unfiltered signals, P-DWT Lv.1A, P-DWT Lv.3D, and P-DWT Lv.4D also showed a balanced number of correct predictions between both classes, their prediction probabilities remained relatively low in the range of 60 - 67%.
Feature selection using the top 3 and 5 features (FS3 and FS5) further enhanced the classification performance. For the unfiltered signals, both FS3 and FS5 increased the number of predictions and improved class balance, with 17 correct predictions for the healthy, and 16 – 20 for the water path. However, similar to the FE case, the prediction probabilities for the unfiltered signal remained low (58 - 63%). A similar trend appeared in the P-DWT Lv.4D results. Although FS improved the number of correct and balanced predictions, the prediction probabilities remained moderate (65 - 73%). P-DWT Lv.1D consistently produced high prediction probabilities (88 – 95%), while maintaining an equal number of correct predictions for both classes (18 each). In contrast, P-DWT Lv.1A and P-DWT Lv.3D resulted in a lower number and an unbalanced number of correct predictions with lower prediction probabilities (53 – 56%).
Overall, detail coefficients, particularly Lv.1D, maintain the high-frequency components associated with internal reflections, voids, and defects. These high-frequency features are highly sensitive to changes in material continuity and acoustic impedance35,36), which can be used to distinguish healthy and water path conditions. The application of high-frequency coefficients corresponds with findings from other researchers who use high-frequency ultrasonic components to improve defect detection accuracy37–39). In contrast, P-DWT Lv.1A showed relatively weak classification performance. This is because approximation coefficients represent low-frequency, global waveform trends, which are less sensitive to localized defects. Whilst higher detail levels (Lv.3D and Lv.4D) tend to over-smooth the signal and attenuate critical high-frequency components necessary for distinguishing healthy and water path conditions.
(3) Analysis of field specimens
a) Semi-supervised learning for field specimens
To validate the performance of the classification model, the trained model was applied to field-case signals as unlabeled data, while the laboratory specimens were used as the labeled data. Fig.17 shows the number of correct predictions for B-H and B-WP (out of 6 per specimen), while Fig.18 shows the prediction probabilities.
Similar to the laboratory specimen results, the classification results of field specimens B-H and BWP consistently showed that combining P-DWT filtering with feature extraction and feature selection provides the most reliable classification of healthy and water path conditions in the PC duct. Across all feature sets, the classification of unfiltered signal shows that 0 correct predictions for healthy, and 4 – 6 correct predictions for the water path, with the prediction probability < 60%. Once again, demonstrated that unfiltered signals were difficult to identify and distinguish between both classes. Approximation coefficient (P-DWT Lv.1A) also produced unbalanced classification for time series and FE data sets, while for FS3 and FS5 data sets, the correct predictions decreased to 2, with prediction probability in a low range between 51 – 56%. As for the P-DWT Lv.1D, the high-frequency can distinguish better between the two classes, especially when using FE and FS. The prediction probabilities increased by 15 - 30% from the time series, and the number of correct predictions was balanced and high between both classes (5 – 6 correct predictions for each class). However, P-DWT Lv.2D resulted in nearly the same prediction probabilities as P-DWT Lv.1D, but the number of correct predictions was unbalanced, especially for the healthy condition, with only 1 correct prediction. P-DWT Lv.3 and P-DWT Lv.4 also show that over-smoothing the wavelet reduces the critical information to distinguish between both classes with very unbalanced predictions (high in one class, low in the other class) with lower prediction probabilities in the range of 52 - 61%.
The last field specimen used to validate the classification model was specimen C. Fig. 19 presents the X-ray scan of specimen C40). In the middle region, particularly around the reinforcement bar, no spots were observed that could be identified as defects.
Meanwhile, several spots appear in the front region, which may indicate the presence of voids or water paths within the duct. These spots are relatively small and not clearly distinguishable, making it difficult to do the visual identification. Therefore, the classification model will help to evaluate specimen C. The PAUT was conducted by scanning 3 locations in the middle region, which were assumed to be healthy, and 5 locations in the front region, which were assumed to correspond to the water path condition.
Table 2 and Fig. 20 show the number of correct predictions and prediction probabilities for specimen C, respectively, where the classification results mostly show the same trend as specimen B. Across all feature sets, the unfiltered signal generally resulted 80% correct prediction for the water path conditions, although the prediction probabilities were below 60%. In contrast, the healthy condition was not correctly identified. This trend was also produced by the P-DWT Lv.2, but with moderate prediction probabilities for the water path class. The P-DWT Lv.1A, Lv.3D, and Lv.4D also show poor performances, resulting in unbalanced and low correct predictions with low prediction probability (50 - 60%). In contrast, P-DWT Lv.1D demonstrated consistent performance across both FE and FS. It correctly identified all healthy signals and achieved 4 – 5 correct predictions for the water path signals, with high prediction probabilities in the range of 91 - 95%.
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Although the number of field samples was limited and not sufficient for a comprehensive assessment of statistical generalizability, the results indicate that the proposed method can be effectively applied to PAUT data in practical inspection scenarios.
b) Percentage probability differences due to RMW
To determine the final label of the unlabeled data, the class with the highest probability was selected as the predicted label. Fig. 21 and Fig. 22 present the average percentage probability differences from the same signals when filtered using different RMWs, where Fig. 21 corresponds to specimen B and Fig. 22 corresponds to specimen C. These results highlight how the RMW influences the classification confidence. Consistent with the overall performance, P-DWT Lv.1D produced the highest probability differences across all feature sets for both specimens B and C. Furthermore, applying feature extraction and feature selection increased these differences by up to 90%, demonstrating that using an RMW derived from specimens with similar physical conditions enhanced the probability of prediction. In contrast, the P-DWT Lv.1A, Lv.3D, and Lv.4D, showed probability differences of less than 5%, indicating that these filtered signals produced nearly identical prediction probabilities between the two classes and therefore provide weaker class separability.
c) Images reconstructed from wavelets
The reconstructed images provide a visual comparison derived from healthy and water path wavelets. These images represent the distribution of energy of ultrasonic signals, allowing the structural condition to be interpreted from the shape, intensity, and smoothness of the wavefront. The images were constructed by Kirchhoff linearized inverse scattering methods (LSIM), which is known to be an effective approach for visualizing medium interfaces41). Furthermore, Takeda H. et al.42) investigated the application of low-frequency components for estimating the approximate location of defects. Their study demonstrated that the Kirchhoff approximation can still provide effective defect localization even in the low-frequency range.
To generate each image, multiple signals were required. Therefore, steering the focus point in the x-axis was performed electronically using PAUT, and a total of seven steering points were used, as illustrated by the red line in Fig. 23.
The following discussion focuses on the differences between healthy and water path images based on P-DWT Lv.1D shown in Fig.24 – Fig. 26. The healthy and water path images from specimen B are presented in Fig. 24 and Fig. 25, respectively. While for specimen C, the healthy conditions are shown in the middle region, and the water path conditions in the front region, as shown in Fig. 26.
The signal energy intensity varies between specimens B and C; however, the overall healthy image patterns remain similar. The healthy images from both specimens show the arc-shaped wavefront that appears smooth, with weak and low oscillations surrounding it. This indicates minimal scattering and suggests that no significant discontinuities are interfering with wave propagation. Some healthy images, such as Fig. 24c, show higher scattering and signal intensity compared to the other healthy images. This variation could be related to differences in coupling conditions or probe positioning. Despite these intensity differences, the overall wave shape and energy distribution remain consistent.
In contrast, the water path images show noticeable differences. Although the arc patterns are still visible, the energy distribution becomes more distorted and asymmetric. Several localized high-intensity spots appear, indicating scattering, mode conversion, and energy leakage. These water path images also exhibit more complex interference patterns and secondary reflections, indicating disrupted propagation paths caused by the differences in acoustic impedance between materials within the PC duct. However, at location 5 of specimen C in Fig. 26, the reconstructed image appears relatively free from disturbance and closely resembles a healthy pattern. This location can therefore be interpreted as a healthy part. This observation is consistent with the classification results from specimen C, where 4 out of 5 water path locations were correctly predicted, indicating 1 misclassification corresponding to a healthy section.
Images reconstructed from unfiltered and filtered wavelets for specimen B at locations 1 and 2 are presented in Table 3. As shown in Table 3, the healthy images from the unfiltered signal and PDWT Lv.1A exhibit only slight differences in energy distribution and overall pattern. The wave remains relatively consistent, with no significant distortions. In contrast, P-DWT Lv.1D produced higher signal intensity, particularly in location 2, making the pattern more clearly visible. For the water path images in specimen B, both the unfiltered and filtered signals produced images that exhibit a distorted wave and a secondary reflection, indicating the disrupted propagation due to the water path. However, there are no significant differences observed between the water path images reconstructed from the unfiltered signal and those from filtered signals for this specimen.
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However, the differences become more noticeable when observing the images reconstructed from specimen C. The healthy images reconstructed from the unfiltered signal and P-DWT Lv.1A, shown in Table 4, display similar arc patterns with relatively low energy. In comparison, P-DWT Lv.1D produces a clearer and higher-energy arc, enhancing the visibility of the wavefront.
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The water path images, reconstructed from the unfiltered signal and P-DWT Lv.1A (Table 5), exhibit patterns that closely resemble the healthy images, making it difficult to distinguish between the healthy and water path conditions. In contrast, the PDWT Lv.1D images reveal more noticeable water path characteristics, including disturbed wavefront and secondary reflection. The detail-based constructed images show sharper and more fragmented energy patterns. The high intensity regions are narrower but more irregular, emphasizing subtle distortions introduced by the presence of the water path.
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This study showed that integrating P-DWT filtering with machine learning enhanced the interpretation of PAUT results for distinguishing between healthy and water path conditions in the PC duct. Among all tested configurations, P-DWT Lv.1D consistently delivered the strongest performance, demonstrating reliable generalization on labeled data and stable prediction on unlabeled data. This level of decomposition enhances high-frequency components that are sensitive to internal defects, while still maintaining the main signal information needed for accurate classification. Feature extraction and feature selection further improved model confidence, increasing probability differences by up 90%, especially when the RMW used for filtering closely matched the physical characteristics of the specimen. The consistent trends observed across field specimens confirm the robustness of the proposed methodology.
The imaging results support these findings. When filtered with the healthy RMW, the reconstructed images appear cleaner, smoother, and more coherent, reflecting stable wave propagation. In contrast, images filtered with the water path RMW display disturbed, complex interference patterns and secondary reflections due to scattering and energy loss around the water path. These differences become clearer in P-DWT Lv.1D images, where subtle distortions are more visibly defined. These observations further validate the use of RMWs similar to the physical condition capable of amplifying defect-related features and improving classification accuracy when combined with P-DWT and machine learning.
ACKNOWLEDGMENT: The authors would like to express their sincere gratitude to Eiji Yoshida of the Public Works Research Institute (PWRI) in Tsukuba, Ibaraki, Japan, for his support and assistance.
